In orthodontics, treatments for achieving alignment of malposed teeth in a subject include applying orthodontic appliances to the subject's teeth. One type of orthodontic appliance comprises pre-shaped orthodontic wires attached to brackets which are themselves attached to the teeth of the subject. The wires, also known as archwires, are typically made from shape memory alloys which have the ability to recover their shape after being deformed. Another type of orthodontic appliance comprises orthodontic aligners which are typically worn over the teeth of the top and/or bottom archforms in order to exert loads to the teeth to induce tooth movements or to retain tooth positions. Although they are removable, aligners are typically arranged to be worn for extended periods during the day and/or night.
A typical orthodontic treatment comprises a number of consecutive treatment steps in which different orthodontic appliances are consecutively used to apply different forces to the teeth as the alignment progresses. In the case of archwires and brackets used as the orthodontic appliance, archwires of different shapes and/or stiffness may be used. In the case of aligners, the aligners may have different shapes for applying different forces to the teeth.
In some cases, the treatment steps may be classified as an aligning stage, a levelling stage, a working stage, a finishing stage and a settling stage. In some cases, the treatment steps comprise an initial stage, a transitional stage and a finishing stage. The treatment stages may include an imposed orthodontic action such as rotation or linear movement of one or more teeth, development of the archform, a levelling of the arches, torque control or retention of the position. Generally, the earlier treatment stages apply more gentle forces compared to the later treatment stages.
Computer simulation of the movement of the subject's teeth may be used for planning one or more of the orthodontic treatment steps. During such simulation, movement of the teeth between a start position and a desired position is simulated. However, the simulated movement may prove inaccurate compared to the actual physical movement of the teeth because of potential collisions between the teeth during the movement. This means that the simulated orthodontic treatment does not reflect accurately the actual effect of the orthodontic treatment, making the planning of orthodontic treatments difficult.
Some prior art methods use Bounding Volume Hierarchies algorithms to reduce the number of operations required for collision detection, and for rendering the simulation more cost effective in terms of processing requirements, using 3D models of the teeth represented by polygonal meshes.
In U.S. Pat. No. 9,848,958, three dimensional (3D) mesh model object of teeth of a patient are generated, and bounding boxes are generated around each tooth. Overlapping bounding boxes are taken as an indication of potential occlusion of those teeth.
In U.S. Pat. No. 6,334,853 describes a method for obtaining a dental occlusion map of a 3D virtual computer model of teeth of upper and lower jaws of a mouth. The occlusion map indicates the distances between opposite regions on facing surfaces of opposite teeth of the upper and lower jaws of the mouth. The method includes the steps of determining the distances between opposite regions on opposite teeth of the upper and lower jaws of the mouth, and setting up a correspondence between the determined distances and regions on a mapping surface.
It is desired to provide improved methods and systems for determining orthodontic treatments.